ON REGULARITY OF SOLUTIONS TO AN INTEGRAL SYSTEM ASSOCIATED WITH BESSEL POTENTIALS

摘要

In this paper, we study the regularity of positive solutions to an integral system associatednwith Bessel potentials. It is a natural extension of the work of Chen, Li, and Manin which regularity of solutions to a system of Wolff potentials was proved by using thenmethod of regularity lifting. We will fully use the decay estimate for the Bessel kernelnboth at the origin and the infinity. This integral system is of independent interest since itncoincides with the famous Schr¨odinger type system of two semi-linear fractional partialndifferential equations.